Reversibility of skew Hurwitz series rings

Authors : Fatma KAYNARCA, Muhammed Ali YILDIRIM

Pages : 2074-2083

Doi:10.15672/hujms.679606

View : 15 | Download : 6

Publication Date : 2020-12-08

Article Type : Research Paper

Abstract :We study the reversibility of skew Hurwitz series at zero as a generalization of an $\alpha$-rigid ring, introducing the concept of skew Hurwitz reversibility. A ring $R$ is called skew Hurwitz reversible insert ignore into journalissuearticles values($SH$-reversible, for short);, if the skew Hurwitz series ring $insert ignore into journalissuearticles values(HR,\alpha);$ is reversible i.e. whenever skew Hurwitz series $f, g\in insert ignore into journalissuearticles values(HR,\alpha);$ satisfy $fg=0$, then $gf=0$. We examine some characterizations and extensions of $SH$-reversible rings in relation with several ring theoretic properties which have roles in ring theory.
Keywords : Skew Hurwitz series ring, reversible ring, α rigid ring, matrix ring